Antoine stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground), $x$ seconds after Antoine threw it, is modeled by: $h(x)=-2x^2+4x+16$ How many seconds after being thrown will the ball hit the ground?
Explanation: The ball hits the ground when $h(x)=0$. $\begin{aligned} h(x)&=0 \\\\ -2x^2+4x+16&=0 \\\\ x^2-2x-8&=0 \\\\ (x+2)(x-4)&=0 \\\\ \swarrow &\searrow \\\\ x+2=0\text{ or }&x-4=0 \\\\ x=-2\text{ or }&x=4 \end{aligned}$ We found that $h(x)=0$ for $x=-2$ or $x=4$. Since $x=-2$ doesn't make sense in our context, the only reasonable answer is $x=4$. In conclusion, the ball will hit the ground after $4$ seconds.